Analysis and design of parallel concatenated channel codes for Quantum Key Distribution (QKD) applications

Abstract

Objective of this paper is the study of Quantum Key Distribution (QKD) protocols based on classical error-correcting codes. The Quantum Key Distribution (QKD) systems and related protocols, in particular conditions, can use the classic channel coding techniques, instead of quantum error-correcting codes, both for correcting errors that occurred during the exchange of a cryptographic key between two authorized users, and to allow privacy amplification, in order to make completely vain a possible intruder attempt. The secret key is transmitted over a quantum, and thus safe, channel, characterized by very low transmission rates and high error rates. This channel is safe for the properties of a quantum system, where each measurement on the system perturbs the system itself, allowing the authorized users to “feel” if there is any intruder listening. Moreover, as shown by accurate experimental studies, the communication channel used for quantum key exchange is not able to reach high levels of reliability (the Quantum Bit Error Rate (QBER) takes values between 0.05 and 0.11), both because of the inherent characteristics of the system, and of the presence of a possible attacker. Thus, in order to obtain acceptable residual error rates, it is necessary to use a parallel classical and public channel, conversely characterized by high transmission rates and low error rates, on which to transmit only the redundancy bits of systematic channel codes with performance possibly close to the capacity limit.